Question 5
A magic triangle consists of several circles in a triangular configuration and are filled with consecutive integers starting from $0$. The integer written in a circle that is supported by two other circles below it is the remainder when the sum of the integers in the supporting circles is divided by the number of circles of the triangle. Moreover, the integer in the bottom leftmost circle should be always less than the integer in the bottom rightmost circle. The diagram below shows an example of a triangle with three circles such that the only division $(1+2)\div3$ leaves a remainder of $0$.
(a) Write down all magic triangles with six circles. (2 marks)
(b) Write down all magic triangles with ten circles. (4 marks)
(a) Write down all magic triangles with six circles. (2 marks)
(b) Write down all magic triangles with ten circles. (4 marks)